A 0.50 kg object rests on a frictionless horizontal countertop, where it is attached to a massless spring whose k-value equals 22.0 N/m. Let x be the displacement, where x = 0 is the equilibrium position and x > 0 when the spring is stretched. The object is pushed, and the spring compressed, until xi = −4.00 cm. It then is released from rest and undergoes simple harmonic motion. How fast is the object moving (in m/s) when the spring is momentarily compressed by 2.00 cm (that is, when x = −2.00 cm)? How fast is the object moving (in m/s) whenever the spring is extended by 2.00 cm (that is, when passing through x = +2.00 cm)? Find the magnitude of the displacement (in cm) at which the object moves with one-half of the maximum speed.
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
A 0.50 kg object rests on a frictionless horizontal countertop, where it is attached to a massless spring whose k-value equals 22.0 N/m. Let x be the displacement, where
is the equilibrium position and
when the spring is stretched. The object is pushed, and the spring compressed, until
It then is released from rest and undergoes
How fast is the object moving (in m/s) when the spring is momentarily compressed by 2.00 cm (that is, when
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